Problem: What is the value of the expression $5^3 - 3 \times 5^2 + 3 \times 5 - 1$?
Answer: Simplify, remembering the exponents take priority over multiplication and multiplication takes priority over addition or subtraction. \begin{align*}
5^3-3\times 5^2+3\times5-1&=125-3\times25+15-1 \\
&=125-75+14 \\
&= 50+14 \\
&= \boxed{64}.
\end{align*}